What is the Greatest Common Factor of 1200 and 1208?

Greatest common factor (GCF) of 1200 and 1208 is 8.

GCF(1200,1208) = 8

We will now calculate the prime factors of 1200 and 1208, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1200 and 1208.

How to find the GCF of 1200 and 1208?

We will first find the prime factorization of 1200 and 1208. After we will calculate the factors of 1200 and 1208 and find the biggest common factor number .

Step-1: Prime Factorization of 1200

Prime factors of 1200 are 2, 3, 5. Prime factorization of 1200 in exponential form is:

1200 = 2⁴ × 3¹ × 5²

Step-2: Prime Factorization of 1208

Prime factors of 1208 are 2, 151. Prime factorization of 1208 in exponential form is:

1208 = 2³ × 151¹

Step-3: Factors of 1200

List of positive integer factors of 1200 that divides 1200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600

Step-4: Factors of 1208

List of positive integer factors of 1208 that divides 1200 without a remainder.

1, 2, 4, 8, 151, 302, 604

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1200 and 1208. The biggest common factor number is the GCF number.
So the greatest common factor 1200 and 1208 is 8.

Also check out the Least Common Multiple of 1200 and 1208